where the two maps defining the coequalizer arise from the simplicial identity \(s_is_{j-1} = s_{j}s_i\)  if \(i<j\)  (see for example V Lemma 1.1 and VII Remark 1.8 of [1]}).
It is well known that \(L_0X = \emptyset \) , \(L_1X = X_0\)  and \(L_2X = X_1\cup _{X_0} X_1\) .
We will need a decomposition of the latching object \(L_nX\)  for any \(n\ge 0\) .
